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Consider penny stocks. They are a poor investment in terms of expected return (unless you have secret alpha). But they provide a small chance of very high returns, meaning they operate like lottery tickets. This isn't a mispricing - some people like lottery tickets, and so bid up the price until they become a poor investment in terms of expected return (problem for the CAPM, not for the EMH). So you can systematically lose money by taking the "wrong" side, and buying penny stocks.
Does that count as an example, or does that violate your "risk-adjusted terms" assumption? I think we have to be careful about what frictions we throw out. If we are too aggressive in throwing out notions like an "equity premium," or hedging, or options, or market segmentation, or irreducible risk, or different tolerances to risk, we will throw out the stuff that causes financial markets to exist. An infinite frictionless plane is a useful thought experiment, but you can't then complain that a car can't drive on such a plane.
Yes, we have to be quite careful here.
Let's take penny stocks. First, there is no exception for them in the EMH so if it holds, the penny stocks, like any other security, must not provide a "free" opportunity to make money.
Second, when you say they are "a poor investment in terms of expected return", do you actually mean expected return? Because it's a single number which has nothing do with risk. A lottery can perfectly well have a positive expected return even if your chance of getting a positive return is very small. The distributio... (read more)